Figure 10-88 shows the example network of four resistors
and a voltage source. With a few simple calculations,
a formula for determining the voltage divisions
in a series circuit can be determined.

The voltage drop across any particular resistor shall
be called EX, where the subscript x is the value of a
particular resistor (1, 2, 3, or 4). Using Ohmís law, the
voltage drop across any resistor can be determined.

Ohmís law: EX = I (RX)

As seen earlier in the text, the current is equal to the
source voltage divided by the total resistance of the
series circuit.

Current: I = ES/RT

The current equation can now be substituted into the
equation for Ohmís law.

Substitute: Ex =(Es/Rt)(Rx)
Algebraic rearrange: Ex =(Rx/Rt)(Es)

This equation is the general voltage divider formula.
The explanation of this formula is that the voltage
drop across any resistor or combination of resistors
in a series circuit is equal to the ratio of the resistance
value to the total resistance, divided by the value of
the source voltage. Figure 10-89 illustrates this with a
network of three resistors and one voltage source.